Large-N limit and contact terms in unbroken YM_4

Abstract

I characterize the structure of the master field for $F_{z\bar{z}}^0$ in $SU(\infty )$-$Y{M}_4$ on a product of two Riemann surfaces $Z\times W$ in the gauge $F_{z\bar{z}}^{ch}=0$ as the sum of a `bulk' constant term and of delta-like `contact' terms.\\ The contact terms may occur because the localization of the functional integral at $N=\infty$ on a master orbit of a constant connection under the action of singular gauge transformations is still compatible with the large-$N$ factorization and translational invariance.\\ In addition I argue that if the gauge group is unbroken and there is a mass gap, that is if the theory confines, the functional measure at $N=\infty$, in the gauge $F_{z\bar{z}}^{ch}=0$, must be localized on the moduli space of flat connections with punctures on $Z\times W$.

8 pages, latex, no figures